Functional magnetic resonance imaging (fMRI) is a crucial technology for
gaining insights into cognitive processes in humans. Data amassed from fMRI
measurements result in volumetric data sets that vary over time. However,
analysing such data presents a challenge due to the large degree of noise and
person-to-person variation in how information is represented in the brain. To
address this challenge, we present a novel topological approach that encodes
each time point in an fMRI data set as a persistence diagram of topological
features, i.e. high-dimensional voids present in the data. This representation
naturally does not rely on voxel-by-voxel correspondence and is robust to
noise. We show that these time-varying persistence diagrams can be clustered to
find meaningful groupings between participants, and that they are also useful
in studying within-subject brain state trajectories of subjects performing a
particular task. Here, we apply both clustering and trajectory analysis
techniques to a group of participants watching the movie 'Partly Cloudy'. We
observe significant differences in both brain state trajectories and overall
topological activity between adults and children watching the same movie.

使用拓扑学方法编码 fMRI 数据检测时间点后高维空间极小值的并归图，以此来处理数据集中的噪音及人与人之间的差异，并开发了一种聚类和轨迹分析的技术，成功分析儿童和成人在观看电影 “Partly Cloudy” 时的大脑状态和拓扑活动。